Fatigue crack propagation in aluminium alloy foams

International Journal of Fatigue 23 (2001) 375–382www.elsevier.com/locate/ijfatigue

Fatigue crack propagation in aluminium alloy foams

O.B. Olurin, K.Y.G. McCullough, N.A. Fleck*, M.F. AshbyUniversity of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, UK

Received 17 July 2000; accepted 15 January 2001

Abstract

The mode I fatigue crack propagation (FCP) response of the closed-cell aluminium alloy foams Alulight and Alporas have beenmeasured for a relative density in the range 0.1 to 0.4. The validity of linear elastic fracture mechanics (LEFM) to characterise thefatigue crack propagation (FCP) response is demonstrated, andK-increasing andK-decreasing tests are used to determine the fullshape of the FCP response. The classical sigmoidal variation of log da/dN with log DK is evident, with a Paris-law exponentm=20for Alulight and m=25 for Alporas. The effects of relative density, mean stress and a single peak overload on the FCP responseare investigated. The study concludes by analysing the mechanism of fatigue crack growth; it is suggested that the fatigue crackgrowth rate is controlled by the progressive degradation of crack bridging by fatigue failure of the cell edges behind the crack tip. 2001 Elsevier Science Ltd. All rights reserved.

Keywords:Aluminium foams; Fatigue crack propagation; Small-scale bridging

1. Introduction

Recent developments in manufacturing methods [1–5] have given rise to a range of commercially viablemetallic foams. Two of these — Alulight1 and Alp-oras2 — are the subject of the present study. Alulight isproduced by a powder metallurgy route, and is availablein cylinders or panels with a relative density rangingfrom 0.1 to 0.4, and in a wide range of compositions,including the Al–Si casting range of alloys. Alporas iscommercially available in plate form, of compositionAl–Ca1.5–Ti1.5 (wt%), and with a relative density in therange 0.08 to 0.15. It is manufactured by a batch castingprocess; like Alulight, the foaming process is by thermaldecomposition of titanium hydride, with the titaniumremaining in solution.

The successful implementation of metallic foams forstructural applications, such as the cores of sandwichpanels, is dependent upon an understanding of their

* Corresponding author. Tel.:+44-1223-332650; fax:+44-1223-765046.

E-mail address:[email protected] (N.A. Fleck).1 Supplier: Mepura Metallpulvergesellschaft mbH, Ranshofen, A-

5282 Braunau–Ranshofen, Austria.2 Supplier: Shinko Wire Company Ltd, 10-1, Nakahama-machi,

Amagasaki-shi, 660 Japan.

0142-1123/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S0142-1123 (01)00010-X

mechanical properties including their resistance tofatigue crack growth. Recent tests [6–8] to measure thestress–life fatigue behaviour of uncracked metallic foamshave shown that the Alulight and Alporas closed-cellaluminium-based foams have promising fatigue proper-ties, with about the same ratio of cyclic strength to mon-otonic strength as that of solid aluminium alloys.

Fatigue crack growth, by contrast, is unexplored: thedependence of crack growth rate da/dN upon the stressintensity rangeDK is not known. In the present study,the validity of using linear elastic fracture mechanics(LEFM) to characterise the applied fatigue loading isdemonstrated andK-increasing andK-decreasing testsare used to determine the fatigue crack propagation(FCP) response. The FCP thresholdDKth is measuredand the effects of relative density, mean applied stressand a single peak overload on the FCP response areevaluated. The extent of a crack bridging zone and themicromechanism of crack growth are also determined.

2. Material specification and experimentalprocedure

Rectangular plates of Alulight Al–Mg1–Si0.6 and Al–Mg1–Si10 foams were manufactured to the dimensions145 mm by 145 mm by 9 mm, with a fully dense skin

376 O.B. Olurin et al. / International Journal of Fatigue 23 (2001) 375–382

of thickness of the order of 1–2 mm. Since the primaryfocus of this study is the effect of foam density and com-position upon the FCP response, the skins were removedby wire electro-discharge machining, giving a net speci-men thicknessB of 7.5 mm (approximately 10 cells).The Alporas foam was obtained from the material sup-plier in blocks of dimensions 0.5 m×0.5m×50 mm; eachblock was of uniform density and was electro-dischargemachined to a thickness of 25 mm.

Compact tension (CT) specimens of widthW=50 mmfor the Alulight specimens and widthW=100 mm forthe Alporas specimens were electro-discharge machinedfrom the as-received blocks. The relative densityr̄ ofthe as-machined specimens wasr̄=0.1 to 0.4 for Alulightand r̄=0.08 to 0.15 for Alporas. (The precise value ofr̄ for each specimen was obtained by weighing to anaccuracy of four significant figures.) Themeancell sizel of Alulight foams varies with relative density accordingto the relation [9,10]

l<l0(122.22r̄), (1)

wherel0=2.25 mm. For example,l<1.5 mm for a foamof relative densityr̄=0.15, whereasl<0.5 mm for a foamof relative densityr̄=0.35. For Alporas, the average cellsize equals 3.5 mm for all densities.

The compact tension specimens were reinforced in thevicinity of the loading holes by Tufnol facings of thick-ness 3 mm for Alulight and 5 mm for Alporas to preventpull-out of the loading pins. The fatigue tests were per-formed at room temperature using a servo-hydraulic testmachine in sinusoidal load control at a frequency of 20Hz, from an initial notch length ofa0/W=0.3 and rootradius of 0.05 mm. We note in passing that preliminarytests confirmed that the fatigue crack propagationresponse was independent of the loading frequency overthe range 0.1–50 Hz. We shall argue below thatDK canbe used to characterise the fatigue loading of the Alulightand Alporas foams specimens. TheK-calibration for theCT geometry as given by ASTM E647-95 [11] wasemployed. On writing the maximum and minimum loadsin each fatigue cycle asPmax andPmin, respectively, theload ratioR is defined byR=Pmin/Pmax.

An evaluation of the FCP response relies upon anaccurate measurement of crack growth. Visual obser-vations using a travelling microscope revealed the pres-ence of a single dominant fatigue crack, with intermittentbridging along its wake. The direct current (DC) poten-tial drop method was used to monitor crack extensionsince, for fully dense metals, it can determine crackgrowth to an accuracy of about 0.01 mm [12]. Theapparatus adopted here is illustrated in Fig. 1. Additionalexperimental details are given in Ref. [10]. Crack lengthmeasurements from a travelling microscope and from theback-face compliance technique [13] were used to checkthe accuracy of the potential drop readings. The meas-ured crack length by potential drop, back-face com-

Fig. 1. Test apparatus.

pliance and visual observation were all in good agree-ment, such that the deduced crack growth rate da/dN ata given DK level agreed to within 10% for the threemethods. The potential drop method was used as the pri-mary method for logging crack length versus cycles. Thecrack growth rate da/dN was calculated by a movingquadratic fit to thea–N data, in accordance with the stan-dard ASTM E647-95 [11].

3. Validity of using K to characterise the appliedfatigue loading

Recent studies on the fracture toughness of Alulight[10] and Alporas [14] made use of compact tensionspecimens of widthW=50 mm and 100 mm; in thesetests a zone of crack bridging developed over about fourcell dimensions from the notch root to the growing cracktip, with full plastic collapse across the uncracked liga-ment. Consequently, the conditions of small-scale bridg-ing (SSB) and small-scale yielding (SSY) do not apply,and the conditions at the crack tip cannot be character-ised simply in terms of the applied stress intensityK. Incontrast, we shall show for similar specimens subjectedto fatigue loading that both SSY and SSB assumptionshold, andDK can be used to characterise the fatigueresponse.

3.1. Validity of small-scale yielding

Conformity with the small-scale yielding assumptionis usually ensured by checking that both the uncrackedligament (W2a) and the crack lengtha of a compacttension specimen satisfy

(W2a, a)$2.5SDK2spl

D2

, (2)

where DK is the stress intensity range of the fatiguecycle andspl is the (tensile) monotonic yield strength ofthe specimen. This is an extension of the usual specimensize criterion in a fracture toughness test, with the role

377O.B. Olurin et al. / International Journal of Fatigue 23 (2001) 375–382

of Kmax replaced byDK and the monotonic yield strengthspl replaced by 2spl in order to estimate the cyclic plasticzone size [15]. This criterion was satisfied for bothmaterials in all fatigue tests. Since the cyclic plastic zoneis of magnitude (1/π)(DK/2spl)2, we conclude that thecyclic plastic zone is much less than the leading speci-men dimensions, and so small-scale yielding con-ditions pertain.

3.2. Validity of small-scale bridging

The extent of crack bridging in the wake of a growingfatigue crack was determined by direct visual obser-vation of the fatigue crack. A scanning electron micro-graph of the side face of an Alulight specimen is shownin Fig. 2, with the position of the crack tip indicated. Asmall bridging zone (of dimension one cell) existsbehind the crack tip, such that the cell faces have crackedbut the cell edges have not. (This is consistent with thenotion that the cell faces undergo membrane tension,whereas the cell edges deform in bending [6].) A similarexamination of cracked Alporas specimens also revealeda bridging zone of length about one cell size.

Additional support for the magnitude of the bridgingzone was obtained by interrupting several tests and byremoving the crack wake using a jeweller’s saw. Poten-tial drop and back-face compliance measurementsrevealed that the apparent crack length only began toincrease when the saw had advanced to within one celldimension behind the optically observed crack tip, indi-cating complete crack face separation except over theshort bridging zone. It is concluded that small-scalebridging (SSB) conditions prevail in fatigue crackgrowth for both foams.

Fig. 2. Scanning electron micrograph of a cracked compact tension specimen of Alulight foam, of composition Al–Mg1–Si0.6 withr̄=0.29. Thecrack has grownDa=8 mm at 1025 mm/cycle, by applying a constantDK=1.12 MPa m1/2 with R=0.1.

4. Results

4.1. Typical da/dN versusDK response

In line with the recommendations of ASTM E647-95[11], three forms of fatigue test were performed:

1. K-increasing tests, used to measure crack growth ratesda/dN.1025 mm/cycle. In these tests, performed at aconstant load amplitude (constantDP), DK wasallowed to increase as the crack length increases.

2. K-decreasing tests, used to measure crack growthrates da/dN,1025 mm/cycle. These tests were perfor-med at a constant normalisedK-gradientc=(1/K)(dK/da)=20.08 mm21 by manual load shed-ding at crack growth intervals ofDa=0.5 mm, inaccordance with ASTM E647-95 [11]. Loads wereshed until no crack growth (i.e., less than 0.01 mm)was detected over 107 cycles.

3. K-constant tests, used to investigate bridging of thecrack wake and the effect of a single peak overloadon the FCP response. The details are the same as forthe K-decreasing tests, but withc=0.

Fig. 3 shows typical fatigue crack propagation results forspecimens of relative densityr̄=0.19, tested at the loadratio R=0.1. It is clear from this figure that the crackgrowth rate da/dN is a unique function ofDK, and inde-pendent of whetherK is increasing, decreasing or con-stant during the tests. The classic sigmoidal variation oflog da/dN with log DK is evident, with a Paris-lawexponentm<20.


Fig. 3. Comparison of da/dN from K-increasing,K-decreasing andK-constant tests. Tests were performed atR=0.1 on compact tensionspecimens of Alulight foam, of composition Al–Mg1–Si0.6 withr̄=0.19.

4.2. Determination of the fatigue crack propagationthreshold,DKth

From Fig. 3, the relationship between log da/dN andlog DK becomes non-linear for an average crack growthincrement of less than about 5×1027 mm/cycle. The stan-dard ASTM E647-95 [11] suggests an arbitrary oper-ational definition of the threshold stress intensity rangeDKth as that value of DK which corresponds toda/dN=1×1028 mm/cycle. However, FCP rates belowda/dN=5×1028 mm/cycle were not achieved with Alu-light: when DK was reduced to investigate these rates,no crack growth was evident for 107 cycles to withinthe resolution of the crack extension measurements (0.01mm). In such cases, theDK at which no crack growthoccurred can be defined asDKth (see, for example,Suresh [15]). For the results shown in Fig. 3 this corre-sponds to a threshold value ofDKth=0.40 MPa m1/2.However, given the sensitivity of da/dN to DK and thescatter in growth rates exhibited by apparently identicalspecimens, a more conservative value forDKth might beconsidered appropriate for design purposes. A simpleconservative estimate can be attained by extrapolatingthe linear regime of the Paris curve down to da/dN=1028

mm/cycle and taking the correspondingDK to beDKth.This method has the added benefit of allowing an oper-ational definition ofDKth from a (time-saving)K-increas-ing test. For the results shown in Fig. 3, the extrapolationmethod impliesDKth=0.34 MPa m1/2, which is only 15%less than the measured value of 0.40 MPa m1/2.

4.3. Effect of silicon content of Alulight on the fatiguecrack propagation response

In order to investigate the effect of silicon content ofAlulight upon the da/dN versusDK response,K-increas-ing tests were performed on compact tension specimensof the Al–Mg1–Si0.6 and the Al–Mg1–Si10 foams. Fig.4 shows typical results, plotted on double log axes, fromspecimens of relative densityr̄=0.23 tested atR=0.1. Forboth compositions of foam, the observed slope wasm<20; however, Al–Mg1–Si10 has a lower fatigueresistance than the Al–Mg1–Si0.6 foam, consistent withits lower fracture toughness [10].

4.4. Effect of relative densityr̄ on the fatigue crackpropagation response

The effect of relative density upon the da/dN versusDK response is shown in Fig. 5(a) for Al–Mg1–Si0.6Alulight and in Fig. 5(b) for Alporas, atR=0.1. For eachof the densities studied, the shape of the da/dN versusDK response is qualitatively similar to that shown in Fig.3, with a Paris-law exponentm<20 for Alulight andm<25 for Alporas. As expected, for a given crackgrowth rate, the stress intensity rangeDK increases withincreasingr̄, see Fig. 5. In Fig. 6, theDK correspondingto da/dN=1024 mm/cycle is cross-plotted againstr̄ usinglog–log axes. Power-law fits with an exponent of 1.71for Alulight and 1.60 for Alporas adequately describethe responses. In similar fashion, the steady-state frac-ture toughnessKss in monotonic fracture tests scaleswith r̄1.75 for both Alulight and Alporas [10,14]. (We

Fig. 4. Effect of silicon content on the da/dN versusDK response.K-increasing tests atR=0.1 on compact tension specimens of Alulightfoam with r̄=0.23.


Fig. 5. Effect of relative densityr̄ on the da/dN versusDK responseat R=0.1 for (a) Alulight foam and (b) Alporas foam. The data forAlulight of relative densityr̄=0.19 are obtained fromK-decreasingtests at low growth rates, and fromK-increasing tests at high growthrates.

remind the reader thatKss is the asymptotic, steady-statevalue of fracture toughness after substantial crackgrowth in a monotonic toughness test.)

In Fig. 7, the crack growth rate data of Fig. 5 are re-plotted against DK/r̄1.71 for Alulight and againstDK/r̄1.60 for Alporas, using log–log axes. For each foam,the data collapse on to a single curve, to within materialscatter. In the Paris regime of the graph, the followingpower-law fit adequately summarises the FCP response

Fig. 6. Effect of relative densityr̄ on the stress intensity rangeDKrequired to give a crack growth rate da/dN=1024 mm/cycle for Alulightand Alporas.

of the Al–Mg1–Si0.6 Alulight foam over a densityrange 0.15,r̄,0.32

dadN

5SdadND0

S DKr̄1.71DK0

D20

, (3)

and in like manner for Alporas over 0.08,r̄,0.15,

dadN

5SdadND0

S DKr̄1.60DK0

D25

. (4)

With the choice (da/dN)0=1024 mm/cycle we haveDK0=10.5 MPa m1/2 for Alulight, and DK0=9.78 MPam1/2 for Alporas.

4.5. Effect of mean stress on the fatigue crackpropagation response

Exploratory tests were conducted to examine theeffect of mean stress (characterised by the load ratio,R=Pmin/Pmax) on the FCP response. The FCP rates fromK-increasing tests atR=0.1, 0.3 and 0.5 are compared inFig. 8 for Al–Mg1–Si0.6 Alulight and Alporas foams. Itis noted that an increase inR value from 0.1 to 0.5 morethan doubles the slopem of the crack resistance curves,and the effect of mean stress can be captured approxi-mately by using√DKKmax as the combined loading para-meter.

4.6. Effect of a single peak overload on the fatiguecrack propagation response

In order to investigate the effect of a single peak over-load on the FCP response, constantDK tests, interrupted


Fig. 7. (a) Effect of relative density on the da/dN versusDK/r̄1.71

response of Alulight foam; taking (da/dN)0=1024 mm/cycle givesDK0=10.5 MPa m1/2. (b) Effect of relative density on the da/dN versusDK/r̄1.60 response of Alporas foam; taking (da/dN)0=1024 mm/cyclegives DK0=9.78 MPa m1/2.

by a single peak overload, were performed on compacttension specimens of the Al–Mg1–Si0.6 Alulight andAlporas foams atR=0.1. Fig. 9(a) presents the resultsfor two Alulight specimens (r̄=0.30) which were testedat the baseline stress intensity ranges ofDK=1.40 MPam1/2 andDK=1.32 MPa m1/2, while Fig. 9(b) shows thecase for Alporas (r̄=0.08) tested atDK=0.12 MPa m1/2.

In each case, the crack was grown at the baselinestress intensity range for several mm before overloadsof rangeDKOL=1.8DK and 1.5DK were applied to theAlulight and Alporas, respectively. The baseline loading

Fig. 8. Effect of load ratioR on the da/dN versus√DKKmax response.K-increasing tests on compact tension specimens of Alporas foam(open symbols) and Alulight foam, composition Al–Mg1–Si0.6 (fullsymbols).

was then resumed. Throughout, the crack length wasmeasured using the DC potential drop method and gavethe same crack length evolution as the back-face com-pliance technique and visual observation using a travel-ling microscope. In all cases, the single peak overloadcaused the crack to advance by 1–2 mm, but once base-line loading had been resumed the growth rate returnedto its pre-overload value. To within the resolution of thecrack extension measurements, neither crack retardationnor crack acceleration was evident. It was not possibleto apply larger overloads due to the low toughness ofthe foams.

We recall that for fully dense metals, crack growthretardation occurs over a crack extension approximatelyequal to the overload plastic zone size,rOL

rOL<1πSKOL

splD2

, (5)

whereKOL is the peak stress intensity factor at overload.On substituting values, we find thatrOL<70–80 mm forthe Alulight andrOL<5 mm for the Alporas specimens.Since the ligament width of the Alulight is about 25 mm,this implies that the overload produced net section yield-ing, invalidating the use ofK as the loading parameterfor the overload cycle. The tests remain useful, however,as an exploratory means of assessing load interactioneffects under variable-amplitude loading. It is concludedthat overloads do not induce crack growth retardation inthese foams. This is not surprising, as we shall arguebelow that the crack advance mechanism is by fatiguefailure of the cell edges behind the crack tip. In contrast,


Fig. 9. Effect of a single peak overload on da/dN. K-constant testsat R=0.1 on compact tension specimens of (a) Alulight foam, compo-sition Al–Mg1–Si0.6 withr̄=0.30, and (b) Alporas foam,r̄=0.08.

load interaction effects in fully dense alloys are due topremature crack closure as the crack advances into theoverload plastic zone (see, for example, [16]).

5. The mechanism of fatigue crack propagation

Visual observations revealed that fatigue cracks growapproximately along the centreline of the Alulight andAlporas CT specimens, apparently following the weakestpath from cell to cell. Away from the fracture plane, no

cell edge cracking is evident. The main fatigue crackadvances by the sequential failure of cell faces ahead ofthe tip. The cell edges behind the crack tip fail later, andthe rate of fatigue failure of the cell edges behind thecrack tip appears to control the overall rate of crackadvance. It is recalled that the extent of crack bridgingis limited to about one cell dimension, as shown in theside view of Alulight, Fig. 2. This interpretation is sup-ported by the fact that the local crack growth rate isretarded when a thick cell edge is encountered and crackgrowth is most rapid through large cells.

The difference in crack bridging is striking for fatiguecrack growth (bridging over a single cell) and monotonicloading (bridging zone of length about four cell sizes).It appears that fatigue failure severely degrades thedegree of crack bridging compared to that observed ina fracture toughness test. This is supported by the factthat the observedDK levels in a fatigue crack growthtest at high growth rates (da/dN<1 mm/cycle) are sig-nificantly smaller than the steady-state fracture tough-ness values (12R)Kss, see Figs. 3 and 7. This phenom-enon of reduced bridging under fatigue loading has beennoted previously for the case of ceramic compositesbridged by metallic fibres [17]; again, fatigue failuredegrades the bridging strength behind an advancingcrack tip.

Examination of the fracture surfaces in a scanningelectron microscope reveals that the crack advanced bymicrovoid coalescence under both cyclic and monotonicloading, see Fig. 10.

6. Concluding remarks

The mode I fatigue crack propagation (FCP) responsesof the closed-cell aluminium-based foams Alulight[compositions Al–Mg1–Si0.6 and Al–Mg1–Si10 (wt%)]and Alporas have been measured for a relative densityin the range 0.1 to 0.4. Linear elastic fracture mechanicscan be used to characterise fatigue crack advance. Theclassic sigmoidal variation of log da/dN with log DK isevident, with a Paris-law exponentm<20–25. The highsensitivity of da/dN to DK suggests that a conventionaldamage-tolerant approach is impractical for design pur-poses; instead, it is recommended that design is basedon keeping the applied stress intensity range below theFCP thresholdDKth.

For a given value of crack growth rate, the resistanceDK scales withr̄1.71 for Alulight and with r̄1.60 for Alp-oras. Increasing the mean applied stress increases theParis-law exponent and, for a givenDK, increases thecrack growth rate da/dN. If the applied fatigue loadingis characterised by√DKKmax, the results for crack growthrate from the R=0.1 and R=0.5 tests intersect atda/dN<1023 mm/cycle. A preliminary study has beenmade of load interaction effects: the injection of a single


Fig. 10. Comparison of scanning electron micrographs of the fracturesurfaces from cyclic and monotonic crack growth tests. Compact ten-sion specimens of Alporas foam,r̄=0.11. (a) Fatigue crack propagationtest (K-increasing,R=0.1) and (b) fracture toughness test.

peak overload into constant baseline loading gives riseto neither crack growth acceleration nor retardation.

Acknowledgements

The authors are grateful to the EPSRC for financialsupport. Additional funding came from DARPA/ONR

through MURI grant number N00014-1-96-1028 on theUltralight Metal Structures project at Harvard Univer-sity. The authors also wish to thank Dr F. Simancik ofMepura for supplying the Alulight foams, Dr T.J. Lu andDr J.E. Huber for constructive comments, and A. Heaverand S. Marshall for their technical assistance.

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Fatigue crack propagation in aluminium alloy foams